01 - Combine the diced mango, pineapple, honey, lime juice, tamari, minced garlic, grated ginger, and smoked paprika in a blender or food processor. Blend until completely smooth.
02 - Transfer 1/4 cup of the blended marinade to a small bowl and set aside for basting during grilling.
03 - Place the chicken breasts in a resealable plastic bag or shallow dish. Pour the remaining marinade over the chicken, ensuring each piece is thoroughly coated. Seal and refrigerate for a minimum of 1 hour, or up to 4 hours for more pronounced flavor.
04 - Preheat an outdoor grill or grill pan to medium-high heat. Lightly oil the grates to prevent sticking.
05 - Remove the chicken from the marinade and discard the used marinade. Pat the chicken lightly dry with paper towels, then brush each breast with olive oil and season generously with salt and pepper.
06 - Place the chicken on the hot grill and cook for 6 to 7 minutes per side. During the last 2 minutes of cooking, baste generously with the reserved marinade. Cook until the internal temperature reaches 165°F.
07 - Transfer the chicken to a cutting board and let it rest for 5 minutes. Slice against the grain and arrange on a platter. Garnish with chopped cilantro and lime wedges before serving.